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Compatible ground-motion time histories for
new national seismic hazard maps
Gail M. Atkinson and Igor A. Beresnev
Abstract: Ground-motion time histories which are compatible with the uniform hazard spectra (UHS) provided by the new
national seismic hazard maps of the Geological Survey of Canada (GSC) are simulated. Time histories are simulated for the
following cities: Halifax, La Malbaie, Québec, Montreal, Ottawa, Toronto, Prince George, Tofino, Vancouver, and Victoria.
The target UHS for the time history simulations are the GSC 5% damped horizontal-component spectra for “firm ground”
(Class B) sites for an annual probability of 1/500. The Canadian Council on Earthquake Engineering is currently considering
the adoption of these maps as the seismological basis for the earthquake design requirements for future editions of the
National Building Code of Canada. It is therefore useful to have compatible time histories for these spectra, in order that
dynamic analysis methods requiring the use of time histories can be employed. The simulated records provide a realistic
representation of ground motion for the earthquake magnitudes and distances that contribute most strongly to hazard at the
selected cities and probability level. For each selected city, two horizontal components are generated for a moderate
earthquake nearby, and two horizontal components are generated for a larger earthquake farther away. These records match
the short- and long-period ends of the target UHS, respectively. These simulations for local and regional crustal earthquakes
are based on a point-source stochastic simulation procedure. For cities in British Columbia, records are also simulated for a
scenario M8.5 earthquake on the Cascadia subduction zone, using a stochastic finite-fault simulation model. Four different
rupture scenarios are considered. The ground motions for this scenario event are not associated with a specific probability
level, but current information suggests that their probability of occurrence is comparable to that of the 1/500 UHS (the
probabilistic analyses performed for the national hazard maps do not explicitly include the Cascadia subduction event). Thus it
would be reasonable to conduct engineering analyses for cities in British Columbia using both the simulated crustal-event
motions and the simulated Cascadia-event motions for the Cascadia event. The time histories simulated for this study are
available free of charge to all interested parties.
Key words: compatible time-histories, seismic hazard, ground motions.
Résumé : Des historiques des mouvements du sol qui sont compatibles avec un spectre uniforme de risques sismiques
(SURS), fournis par les nouvelles cartes nationales de la séismicité de la Commission géologique du Canada (CGC) sont
simulés. Ces historiques sont simulés pour les villes suivantes : Halifax, La Malbaie, Québec, Montréal, Ottawa, Toronto,
Prince George, Tofino, Vancouver et Victoria. L’objectif du SURS pour les simulations temporelles est d’amortir le
composant horizontal du spectre du CGC de 5% pour des sites de « sols compacts » (classe B) pour une probabilité annuelle
de 1/500. Le conseil canadien d’ingénierie parasismique considère actuellement l’adoption de ces cartes comme une base
sismologique pour les exigences en conception parasismique pour les futures éditions du Code national du bâtiment du
Canada. Il s’avère donc utile de posséder des historiques compatibles pour ces spectres, afin que les méthodes d’analyse
dynamique nécessitant l’utilisation d’historiques puissent être employées. Les cas simulés offrent une représentation réaliste
des mouvements du sol pour des magnitudes et distances de tremblement de terres qui contribuent le plus fortement au risque
des villes choisies et au niveau de probabilité. Pour chacune des villes précitées, deux composantes horizontales sont générées
pour un tremblement de terre modéré à proximité, et deux autres composantes horizontales sont générées pour un tremblement
de terre plus important mais également plus éloigné. Ces enregistrements concordent avec les termes sur une courte et sur une
longue période du SURS visé respectivement. Ces simulations de séismes lithoshériques locaux et régionaux sont basées sur
une procédure de simulation stochastique à source ponctuelle. En ce qui concernent les villes de la Colombie Britannique, les
enregistrements sont aussi simulés pour un scénario d’un séisme M8,5 sur la zone de subduction de Cascadia, au moyen d’un
modèle de simulation stochastique à défaut fini. Quatre différents scénarios de rupture furent considérés. Les mouvements du
sol pour ces scénarios ne sont pas associés à un niveau de probabilité spécifique, mais les informations actuelles suggèrent que
leur probabilité d’occurrence soit comparable au SURS 1/500 (l’analyse probabilistique réalisée pour les cartes de la
séismicité du Canada n’inclut pas explicitement l’événement de subduction de Cascadia). Il serait donc raisonnable de mener
des analyses techniques pour les villes de la Colombie Britannique, en utilisant à la fois les mouvements simulés
Received October 1, 1996. Revised manuscript accepted August 25, 1997.
G.M. Atkinson and I.A. Beresnev. Department of Earth Sciences, Carleton University, 1125 Colonel By Drive,
Ottawa, ON K1S 5B6, Canada.
Written discussion of this article is welcomed and will be received by the Editor until August 31, 1998 (address inside front cover).
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Can. J. Civ. Eng. Vol. 25, 1998
d’événements lithosphériques et ceux de la zone de subduction de Cascadia pour simuler l’événement de Cascadia. Les
historiques simulés pour cette étude sont disponibles gratuitement à toute personne intéressée.
Mots clés : historiques compatibles, risque sismique, mouvement du sol.
[Traduit par la rédaction]
Introduction
New national seismic hazard maps have been developed by the
Geological Survey of Canada (GSC) (Adams et al. 1996). The
maps present 5% damped uniform-hazard response spectra
(UHS) for firm ground sites for a number of vibrational periods, at a probability level of 1/500 per annum (p.a.). The Canadian Council on Earthquake Engineering (CANCEE) is
currently considering the adoption of these new maps as the
seismological basis for the earthquake design requirements for
future editions of the National Building Code of Canada
(NBCC). The new maps embody the last 15 years of progress
in seismological information and seismic hazard analysis techniques, and are intended to replace the current zoning maps in
the NBCC, which were developed around 1980.
For buildings to be designed either using the equivalentlateral-force procedures of the NBCC or by a dynamic analysis
using modal analysis procedures, the new hazard maps, used
in conjunction with the NBCC provisions, provide all the required input information for the engineering analyses. In some
cases, however, the engineer may wish to perform a dynamic
analysis based on a time-history method. Time histories that
are equivalent to the UHS given by the seismic hazard maps
are required for such applications; these ground motion records are referred to as compatible time histories.
Obtaining UHS-compatible time histories is not a trivial
task, particularly for the Canadian seismic hazard environment. One approach is to select real recordings that match the
“target” spectrum in a selected period range. However, this
approach is only appropriate when recordings are available for
the magnitude–distance range and tectonic environment that
is causing the hazard. If these conditions cannot be met, then
the selected real records will have no clear relationship to the
ground motion hazard at the site; the motions may not be
physically realizable in terms of frequency content or duration
of motion, for example. Unfortunately, this is the situation for
most of Canada. In particular, for the magnitude–distance
combinations identified in this study as representative of the
GSC 1/500 spectra (Table 1), there are no applicable records
for either eastern or western Canada. Use of California records
to represent these events would be inappropriate; there are
pervasive differences in source, attenuation, and site characteristics between California earthquakes and those in eastern
and western Canada, which profoundly affect the amplitudes
and frequency content of the ground motions (Atkinson 1995a,
1995b; Atkinson and Boore 1997b). Thus “real” earthquake
recordings from California cannot provide “real” records for
Canada.
The alternative in this situation is to simulate suitable records. It is important that the simulation technique be capable
of generating physically realizable records. There are some
well-used engineering simulation programs that generate a
compatible time history directly from a specified response
spectrum (based on no other seismological information). If
these approaches are applied to a uniform-hazard spectrum,
they produce an artificial composite record which is unlike any
actual ground motion that might be experienced; the composite
record is more akin to the simultaneous occurrence of a
number of potentially damaging events. To produce physically
realistic time histories, it is necessary to simulate motions
which not only match the spectrum, but which are representative of motions for specific magnitude–distance scenarios
in the region of interest. Such simulation procedures are well
developed and frequently applied in design of critical facilities
(e.g., Reiter 1990), but are not often employed for the analysis
of ordinary structures.
There is, perhaps, an intuitive reluctance to substitute simulated time histories for real earthquake recordings. There are
apparent differences between simulated and real records, reflecting factors such as non-stationarity of signals due to arrivals of different wave groups, unmodeled signal complexity,
and unmodeled ground motion coda. These factors combine to
make simulated records differ, visually, from many real recordings. Numerous studies have shown, however, that simulated records and real records are functionally equivalent, from
both the linear and nonlinear points of view. For example,
Greig and Atkinson (1993) compared elastic and inelastic
strength demand spectra for 66 records from four eastern Canadian earthquakes (including the Saguenay, Quebec, earthquake of 1988), with the corresponding spectra for simulated
records of the same events and distances. The real records
varied in composition, from near-source records containing
only direct waves, to distant records dominated by complex
surface wave trains; the simulated records were stationary signals. These comparisons showed that the simulated records
provided an adequate basis for estimating both linear and nonlinear effects. This is not surprising, because the real and simulated signals have approximately the same amplitude and
frequency content, and approximately the same duration.
Turkstra and Tallin (1988) reached a similar conclusion based
on comparisons of simulated records with actual time histories
for a number of California earthquakes.
On a philosophical note, it is important to recognize that
recorded time histories are only “real time histories” in the
sense that they represent a past event that actually happened.
They will never be recorded again. Future events, having magnitudes, locations, and rupture characteristics different from
those of past events, will produce records with different ground
motion characteristics. The advantage of the simulation approach lies in generalizing the gross features of past events that
are repeatable (e.g., average amplitudes and frequency content
as a function of magnitude and distance), while building in an
appropriate stochastic element to account for the features of
ground motion which are random. In the context of their future
likelihood of occurrence, simulated records are just as “real”
as past recordings.
It is the purpose of this paper to simulate compatible time
histories for the new 1/500 national seismic hazard maps, for
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a number of cities in eastern and western Canada. The eastern
hazard is derived from local moderate earthquakes and larger
regional events, all within the shallow (h < 30 km) crust. For
the western cities, time histories are simulated for crustal earthquakes, as well as for a M8.5 scenario earthquake along the
Cascadia subduction zone.
Definition of scenario events for the
simulations
Basis for scenario events
The starting point for the simulation of spectrum-compatible
time histories is the definition of scenario events, in terms of
earthquake magnitude and distance. These events should represent the types of earthquakes that are the dominant contributors to the seismic hazard at the site of interest, for the specified
probability level. This study adopts the 1/500 p.a. uniform hazard spectra of Adams et al. (1996) as the foundation for this
selection, for all crustal earthquakes.
Overview of GSC spectra
The spectra of Adams et al., hereafter referred to as the GSC
spectra, were derived from a probabilistic hazard analysis, following the well-known Cornell–McGuire method (Cornell
1968; McGuire 1977; Toro and McGuire 1987; see EERI
(1989) for a review). The basic steps of the analysis are as
follows. First, seismotectonic information is used to define
seismic source zones, which may be areas of diffuse or concentrated seismicity, or specific active faults. Generally, a number
of alternative hypotheses regarding the configuration of these
seismogenic source zones are formulated. For each source
zone, the earthquake catalogue is used to define the magnitude–recurrence relation and its uncertainty; this provides the
description of the frequency of occurrence of events within the
zone, as a function of earthquake magnitude. Ground-motion
relations are defined (along with their uncertainty) to provide
the link between the occurrence of earthquakes within the
zones, and the resulting ground motions at a specified location.
Ground-motion relations can be given in terms of peak ground
acceleration or velocity, or for response spectral ordinates for
given periods of vibration. Within the last 10 years, practice
has shifted to the use of response spectra instead of peak
ground-motion parameters, due to their greater engineering
relevance (EPRI 1986; EERI 1989; Atkinson 1991; Heidebrecht et al. 1994). Thus the GSC maps are based on response
spectral ordinates.
The final step of the hazard analysis is an integration, over
all earthquake magnitudes and distances, of the contributions
to the probability of exceeding specified ground-motion levels
at the site of interest. This is repeated for a number of vibrational periods in order to define the uniform-hazard spectrum,
which is a response spectrum having a specified probability of
exceedence. If an analysis of uncertainty has been carried
throughout the analysis (as for the GSC spectra), then a family
of spectra for each probability level can be defined, representing the confidence with which the probabilistic motions
can be determined. These confidence limits are derived from
the uncertainty in the model parameters that describe the hazard. Thus they represent model uncertainty, as opposed to random variability in the underlying physical processes. Note that
307
random variability is considered explicitly in the hazard integrations, and its effects are thus included in the hazard curves
for all confidence levels.
For critical facilities, one may wish to be 80% or 90% confident that the true hazard curve lies below the adopted value,
and might therefore wish to use 80th or 90th percentile hazard
curves. In the case of the GSC maps, the adopted spectra represent median values (e.g., 50th percentile) for ground motion
with a probability of 1/500 p.a. Generally speaking, median
hazard curves are similar to the “best-estimate” values that
would be obtained if model uncertainty were not included in
the analysis. The GSC spectra are defined for “firm ground”
site conditions, representing Class B sites in the terminology
of Boore et al. (1993); the average shear-wave velocity for
such sites is given as 555 m/s.
Selecting compatible time histories
The uniform-hazard spectrum (UHS) can be thought of as a
composite of the types of earthquakes that contribute most
strongly to the hazard at the specified probability level. In
general, the dominant contributor to the short-period groundmotion hazard comes from small-to-moderate earthquakes at
close distances, whereas larger earthquakes at greater distance
contribute most strongly to the long-period ground-motion
hazard (Reiter 1990; McGuire 1995). As the probability level
is lowered, the dominant effect is to move both the regional
and local contributing earthquakes closer to the site.
To be compatible with the UHS, time histories should be
simulated for the earthquake magnitudes and distances which
dominate the seismic hazard for the selected probability level.
Furthermore, the spectra for the selected records, when taken
as a suite, should approximately match the target UHS response spectrum. These considerations suggest that more than
one type of earthquake will generally be required to match the
target spectrum over the entire period range of interest (assumed to be approximately 0.1–5 s). A typical example might
be a target spectrum which is matched in the 0.1–0.5 s band
by a moment magnitude (M) 5.5 earthquake at distance (R) of
20 km, and matched in the 0.5–5 s band by a M7 earthquake
at R = 70 km. The moderate nearby earthquake would not produce sufficient long-period energy to match the 0.5–5 s band
of the UHS, while the larger distant earthquake would have
lost too much high-frequency energy, due to attenuation, to
match the short-period band. Therefore the structure would
need to be analyzed for both of these earthquakes, unless its
range of response limits this requirement. Note that the peak
ground acceleration of the motion is often not particularly relevant, as it is carried by the highest frequencies in the record,
which may be above the frequency range of structural response. For example, magnitude 3 earthquakes can produce
very large accelerations near the earthquake source, but these
do not cause damage to structures.
A rigorous selection of representative earthquake magnitudes and distances can be made on a site-specific basis by
“de-aggregating” the seismic hazard results (McGuire 1995).
This procedure involves taking apart the integral in the probability calculations that sums the hazard contributions over
magnitude, distance, and random variability in ground-motion
amplitudes (sigma). The relative probability contributions are
examined as functions of these parameters, for each vibrational
period of interest. Time histories can then be selected or simu© 1998 NRC Canada
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Simulated time histories for crustal
earthquakes
Simulation methodology
The stochastic point-source simulation method of Boore
(1983) is used to generate time histories for the crustal earthquakes in both eastern and western Canada. Both the method
Fig. 1. Amplification factor applied in the frequency-domain to
convert simulations for hard-rock sites to simulations for Class B
(firm ground) soil sites. These factors were applied to all
simulations presented in this paper.
0.50
0.45
0.40
Soil factor in log units
lated for the most-likely combinations of magnitude, distance,
and sigma, for a certain period range.
Based on practical experience with these de-aggregations
in a variety of tectonic environments (e.g., Atkinson 1990;
McGuire 1995), the following simplified representation of this
process is adopted:
• The 1/500 UHS for the modeled eastern Canadian sites can
be adequately approximated using an event of M5.5 to
represent the short-period hazard plus an event of M7.0 to
represent the long-period hazard; the distances at which
these events are placed depend on the seismicity rates of
the site area.
• The 1/500 UHS for the modeled western Canadian cities
(all in western B.C.) can be adequately approximated using
an event of M6.0 to represent the short-period hazard plus
an event of M7.2 to represent the long-period hazard; the
distances at which these events are placed depend on the
seismicity rates of the site area. These two scenario events
represent only the hazard due to crustal and subcrustal
earthquakes, and do not include the hazard due to a great
earthquake along the Cascadia subduction zone.
• For the scenario crustal earthquakes in both eastern and
western Canada, ground motions should be simulated for
approximately the median-plus-one-standard-deviation
ground-motion level (e.g., the median level times a factor
of 2), for the stated magnitude and distance. The multiplicative factor of 2.0 on the amplitudes for the given magnitude and distance can be adjusted up or down somewhat
(within about the range from 1.0 to 3.0) as needed to match
the target spectrum. Note that the time histories so obtained
are still representative of the median UHS, because this
factor is applied before the time histories are matched to
the target median UHS. (In other words, the spectra of the
simulated events still match the median UHS.) The purpose of including the factor is to account for typical deaggregation results, which show that the dominant hazard
contributions come from motions that are larger-thanmedian for the given magnitude and distance (e.g., see
McGuire 1995). This reflects amplitude variability in recorded ground motions, which is the most important factor
influencing the relationship between median and 84th percentile motions.
• A great earthquake on the Cascadia subduction zone is
treated as a separate scenario for western cities. This is
consistent with the approach of the GSC; they did not include the Cascadia subduction event in the probabilistic
computations of the UHS, but examined it as a separate
“scenario” event. The adopted magnitude for this scenario
is M8.5 in this paper, slightly larger than the value of M8.2
used by the GSC. Its probability of occurrence has not been
explicitly evaluated, but is believed to be roughly comparable to the probability of the shallow crustal scenarios.
Can. J. Civ. Eng. Vol. 25, 1998
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0
0.01
0.1
1
10
Period (s)
and its application to eastern and western Canada have been
described in detail elsewhere (Atkinson and Boore 1995,
1997a) and will only be summarized here. The method has its
origins in the observation that, on average, high-frequency
ground motions can be accurately modeled as finite-duration
bandlimited Gaussian noise, with an underlying Fourier amplitude spectrum as specified by a simple seismological model of
source and propagation processes (Hanks and McGuire 1981;
Boore 1983; Atkinson and Boore 1995).
The method begins with the generation of a windowed acceleration time series, comprised of random Gaussian noise
with zero mean amplitude, and a mean spectral amplitude of
unity. The duration of the window is specified as a function of
magnitude and distance, based on regional empirical observations. The spectrum of the windowed noise time series is multiplied by a desired Fourier acceleration spectrum; this
spectrum is specified as a function of seismic moment (or moment magnitude, M) and distance, based on a seismological or
empirical model. A point-source representation of source and
propagation is used for the simulations of crustal events: this
is readily justified for the magnitude–distance range of events
that dominate the hazard at the 1/500 p.a. probability level.
The filtered spectrum is then transformed back into the time
domain to yield a simulated earthquake record for that magnitude and distance.
The Fourier amplitude spectrum used to control the amplitude and frequency content of the time history is a product of
the source spectrum as a function of magnitude, its attenuation
with distance, and the amplification by the local site conditions,
as well as by the factor of 2 used to generate motions near the
median-plus-one-standard-deviation level for the given M and R.
For this study, the object is to generate motions for “firm
soil’ conditions (Class B of Boore et al. 1993). The seismological models of source and propagation, which are used to generate the amplitude spectra, are applicable to hard rock
conditions (shear-wave velocity of 2.5–3.5 km/s). This is because the seismograph stations, which recorded the empirical
data on which these models were based, are sited almost exclusively on hard rock, in both eastern and western Canada.
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Table 1. Applicable time histories to match GSC 1/500 p.a. target UHS.
City
Short-period
event
Scale factor for
short-period event
Long-period
event
Scale factor for
long-period event
Halifax; Toronto
La Malbaie
Québec; Montreal; Ottawa
Prince George
Vancouver; Victoria
Tofino
M5.5 at R70
M5.5 at R15
M5.5 at R30
M6 at R70
M6 at R20
M6 at R30
1.2
1.3
0.8
0.7
1.1
1.0
M7 at R300
M7 at R30
M7 at R150
M7.2 at R200
M7.2 at R70
M7.2 at R70
0.6
0.7
0.7
0.7
0.8
0.7
Fig. 2. Target 1/500 p.a. UHS from GSC for Halifax (filled
squares) and Toronto (open squares), and spectra of selected
compatible time histories, multiplied by the stated scaling factor
(the geometric average of the spectra for two horizontal
components for the stated M and R combination is plotted). Solid
line shows spectra for event that matches the short-period end of
the spectrum; dotted line shows spectra for event that matches the
long-period end of the spectrum.
Fig. 3. Target 1/500 p.a. UHS from GSC for Québec (filled
squares), Montreal (open squares), and Ottawa (asterisks), and
spectra of selected compatible time histories, multiplied by the
stated scaling factor (the geometric average of the spectra for two
horizontal components for the stated M and R combination is
plotted). Solid line shows spectra for event that matches the
short-period end of the spectrum; dotted line shows spectra for
event that matches the long-period end of the spectrum.
100
UHS Halifax
UHS Québec
UHS Toronto
UHS Montreal
UHS Ottawa
M5.5 R70 *1.2
M7 R300 *0.6
10
1
0.01
PSA (%g)
PSA (%g)
100
0.1
1
10
Period (s)
The amplitude spectra are therefore multiplied by the soilamplification factors appropriate for Class B sites, shown in
Fig. 1. These factors are adopted from Adams et al. (1996),
and represent a synthesis of empirical and analytical soil response studies. The use of frequency-dependent amplification
factors is consistent with the foundation-factor approach that
is embodied in the NBCC and model U.S. codes (Martin and
Dobry 1994; NEHRP 1994); it is also consistent with observations from California, where the ground-motion database is
large enough to allow such factors to be derived empirically
(e.g., Boore et al. 1993).
The soil amplification factors were derived to convert generic “hard-rock” motions to equivalent motions on Class B
soils. In the methodology of Adams et al. they were only required for the eastern applications. In this study, they are also
applied to the B.C. simulations, since the B.C. simulation
methodology is based on hard-rock motions. The soil factors
have been extended to periods (T) slightly beyond that given
by Adams et al. by assuming constant amplification for T <
0.1 s and for T > 2 s. This is a conservative assumption, since
amplifications eventually tend to unity at both the short- and
long-period ends of the spectrum.
M5.5 R30 *0.8
10
M7 R150 *0.7
1
0.01
0.1
1
10
Period (s)
Eastern Canada
The stochastic point-source simulations for eastern Canada use
the seismological model parameters of Atkinson and Boore
(1995), as amplified by the soil factors shown in Fig. 1, and by
the factor of 2 to generate median-plus-sigma amplitude levels
for the specified M and R. The model was developed specifically for eastern North America, and the model parameters
validated empirically using recordings from over 100 eastern
earthquakes in the magnitude range from 3 to 6.8. In order to
generate time histories that are compatible with the target
UHS, magnitude–distance combinations are sought that will
result in a match in median levels over the period band of
interest — generally by using more than one record for the
analysis, with different records covering different parts of the
period band. Because the exact locations of peaks and troughs
in the generated records are random, structures should be analyzed for more than one record. Accordingly, two time histories have been generated for each event; these can be
considered as two random horizontal components of acceleration.
Time histories are generated for M5.5 and M7.0 earthquakes at hypocentral distances (R) of 15, 20, 30, 50, 70, 100,
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Can. J. Civ. Eng. Vol. 25, 1998
1000
UHS La Malbaie
M5.5 R15 *1.3
100
M7 R30 *0.7
Fig. 5. Example time histories (unscaled) for eastern cities:
(a) M5.5 event at R = 20 km and (b) M7 event at R = 70 km.
40
(a) M5.5 R20
30
20
Acceleration (%g)
Fig. 4. Target 1/500 p.a. UHS from GSC for La Malbaie (filled
squares), and spectra of selected compatible time histories,
multiplied by the stated scaling factor (the geometric average of the
spectra for two horizontal components for the stated M and R
combination is plotted). Solid line shows spectra for event that
matches the short-period end of the spectrum; dotted line shows
spectra for event that matches the long-period end of the spectrum.
10
0
-10
PSA (%g)
-20
-30
-40
-5
10
0
5
10
Time (s)
15
20
5
10
Time (s)
15
20
20
1
0.01
0.1
1
15
10
(b) M7 R70
Period (s)
150, 200, and 300 km (for Class B sites, for motions a factor
of two times the median levels). For each city, the best distance
value for the M5.5 event is selected, such that the average
spectrum for the two simulated records most closely matches
the short-period end of the target UHS spectrum. Similarly, the
best distance value for the M7.0 simulations is determined by
matching the long-period end of the target UHS. The selected
time histories are then scaled up or down by a “fine-tuning”
factor (between 0.6 and 1.3), so as to match the target as
closely as possible. This fine-tuning factor is equivalent to
adjusting the number of standard deviations of the motion from
the median, within the range from 1.2 to 2.6 standard deviations (e.g., 0.6 × 2 to 1.3 × 2). The selected events and finetuning factors are given in Table 1. Figures 2–4 show the
target UHS spectra for the selected eastern cities, and the corresponding spectra for the simulated time histories, as scaled
by the fine-tuning factor; the geometric average of the spectra
of the two horizontal components is plotted.
There is significant overlap in the intermediate-period
range between the spectra of the M5.5 and M7.0 events, but
they may have different effects on the structure due to differences in overall duration and frequency content. In some cases
the target spectra were considered simultaneously for two or
more cities, due to the similarity of their UHS (e.g., target
spectra are not significantly different for Ottawa, Montreal,
and Québec). Figure 5 plots example time histories for the
M5.5 and M7.0 events at selected distances. Notice that the
M5.5 event has a shorter duration and higher frequency content than the more distant M7.0 event.
Western Canada (B.C.)
Simulations for the crustal or subcrustal events of M6.0 and
M7.2 for B.C. are based on the same stochastic point-source
simulation methodology used for eastern Canada. In this case,
however, the seismological model of the earthquake Fourier
Acceleration (%g)
10
5
0
-5
-10
-15
-20
-5
0
amplitude spectrum, as a function of magnitude and distance,
and the duration model are specific to B.C. (Atkinson 1995a).
These models were developed and empirically validated using
records from about 60 B.C. earthquakes of magnitude 3.5 to 7
(see also Atkinson and Boore 1997a). High-frequency attenuation is based on the B.C. kappa value of 0.011 s (Atkinson
1995b).
The available ground-motion database used to validate the
seismological models for B.C. events was, until the introduction of the new GSC three-component broadband network a
few years ago, comprised of vertical-component data; however, it is the horizontal component of motion that is of engineering interest. Fortunately, the horizontal and vertical
components of ground motion are highly correlated; they can
be related through a frequency-dependent ratio (H/V ratio) that
is, for practical purposes, independent of magnitude and distance (e.g., Atkinson 1993). The H/V ratio depends primarily
on site conditions, since near-surface changes in seismic impedance amplify horizontal motions significantly, while leaving vertical component motions largely unaffected
(Theodulidis et al. 1996; Castro et al. 1997). The H/V ratio for
hard-rock seismograph sites in B.C., which were used to derive
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Atkinson and Beresnev
Fig. 6. Target 1/500 p.a. UHS from GSC for Vancouver (filled
squares) and Victoria (open squares), and spectra of selected
compatible time histories, multiplied by the stated scaling factor
(the geometric average of the spectra for two horizontal
components for the stated M and R combination is plotted). Solid
line shows spectra for event that matches the short-period end of
the spectrum; dotted line shows spectra for event that matches the
long-period end of the spectrum.
Fig. 7. Target 1/500 p.a. UHS from GSC for Tofino (filled
squares), and spectra of selected compatible time histories,
multiplied by the stated scaling factor (the geometric average of the
spectra for two horizontal components for the stated M and R
combination is plotted). Solid line shows spectra for event that
matches the short-period end of the spectrum; dotted line shows
spectra for event that matches the long-period end of the spectrum.
100
100
UHS Tofino
UHS Vancouver
M6 R30 *1.0
PSA (%g)
PSA (%g)
UHS Victoria
M6 R20 *1.1
10
M7.2 R70 *0.8
M7.2 R70 *0.7
10
1
0.1
1
0.1
1
Period (s)
10
the regional ground-motion parameters needed for the simulations, was investigated using three-component broadband records of the Duvall earthquake and its aftershocks (Atkinson
1997); this investigation confirmed the applicability of the
adopted model parameters for the horizontal component of
shear radiation. Finally, the fundamental similarities and differences of the vertical and horizontal components may be
noted. P-waves converted from S-waves at the near-surface
boundaries may contribute to the vertical component in a
shear-wave window, while the horizontal component is dominated by the S-radiation. The converted P-wave will nevertheless retain all spectral characteristics of the initial S-wave. The
vertical component can thus be used to represent the characteristics of S-wave propagation without loss of generality, provided the H/V ratio for the recording sites can be estimated.
Using the same procedure as for eastern Canada, the soil
amplification factors of Fig. 1 are applied to the Fourier amplitude spectrum for hard rock, as is the factor of 2 applied to
simulate motions larger than the median for the stated M and
R. The main difference between the eastern and western motions, for a given M and R, is that the eastern motions have
enhanced high-frequency radiation levels. This difference has
been well established empirically (see Atkinson and Boore
1997b).
The procedure used to determine the scenario events for
each city, listed in terms of M and R in Table 1, is the same as
that used for eastern Canada. Figures 6–8 show the target UHS
for the B.C. cities and the average of the selected time histories, scaled by the stated fine-tuning factors. Again, there are
two scenarios for each target spectrum, with two random horizontal components for each scenario, for a total of four time
histories corresponding to each city. Time history analyses
should be performed for all four scenario events for the target
spectrum, in order to ensure compatibility. Figure 9 shows example B.C. time histories. The differences in frequency content between eastern and western motions, and its effects on
1
Period (s)
10
peak ground acceleration, are apparent by comparing Figs. 5
and 9.
Simulations for cascadia subduction
earthquake
Extension of point-source model to finite faults
The validity of the point-source model tends to break down
near the source of large earthquakes, for which the effects of
source–receiver geometry and rupture directivity can be significant. To model ground motions from a great earthquake on
the Cascadia subduction zone, then, requires a simulation
method that incorporates these finite-fault effects. In a finitefault simulation, the large fault plane representing a great Cascadia earthquake is subdivided into smaller parts, each of
which is treated as a point source, and the ground motions at a
specified site are obtained by summing the delayed contributions from all parts of the fault (Hartzell 1978; Kanamori 1979;
Heaton and Hartzell 1989). The shear-wave components of the
seismic radiation are simulated using the procedures given by
Beresnev and Atkinson (1997). Briefly, every subevent is associated with a stochastic point source, with parameters as
described in the previous section. The initiation time of rupture
at each subfault is determined by the propagation speed of the
rupture, as it travels outward radially from the hypocentre.
Heterogeneity of rupture is provided by adding a small random
component to the starting time of rupture for each of the subfaults. Each subsource is allowed to trigger a number of times
in order to provide the correct amount of final slip. This
number is adjusted to conserve the total seismic moment of the
simulated event. The radiation from each subfault is attenuated, using the point-source attenuation model, according to
the distance between the subfault and the site. The total motions at the site contain the summed contributions from all
subsources, appropriately lagged in time according to the geometry of rupture propagation.
The basic assumptions of this study can be compared with
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10
UHS Prince George
M6 R70 *0.7
PSA (%g)
Fig. 9. Example time histories (unscaled) for western cities: (a) M6
event at R = 20 km and (b) M7.2 event at R = 70 km.
20
M7.2 R200 *0.7
(a) M6 R20
15
10
Acceleration (%g)
Fig. 8. Target 1/500 p.a. UHS from GSC for Prince George (filled
squares), and spectra of selected compatible time histories,
multiplied by the stated scaling factor (the geometric average of the
spectra for two horizontal components for the stated M and R
combination is plotted). Solid line shows spectra for event that
matches the short-period end of the spectrum; dotted line shows
spectra for event that matches the long-period end of the spectrum.
5
0
-5
-10
1
-15
-20
-5
0.1
0.1
1
Period (s)
5
10
Time (s)
15
20
5
10
Time (s)
15
20
20
10
15
(b) M7.2 R70
10
Acceleration (%g)
those of previous predictions of ground motion from a hypothetical megathrust earthquake on the Cascadia subduction
zone. There are four such predictions available in the literature,
all for the Seattle region (Youngs et al. 1988; Heaton and
Hartzell 1989; Silva et al. 1990; Cohee et al. 1991). Youngs et
al. (1988) used a theoretical source function to describe movement on the elementary subfaults. Heaton and Hartzell (1989)
and Cohee et al. (1991) used recordings from smaller earthquakes as empirical source functions. The procedure of this
study, and that of Silva et al., is based on a stochastic pointsource representation of the subfault radiation. The approaches
of Youngs et al., Heaton and Hartzell, and Cohee et al. all
require specification of a detailed crustal structure, because
they use theoretical attenuation based on wave propagation
through the crustal structure. By contrast, the adopted modeling procedure, and that of Silva et al., employs an empirical
attenuation operator. Overall, the simulation method employed in this study is closest to that of Silva et al. (1990),
although the approach differs considerably in defining the basic physical parameters of the elementary sources. The advantage of the adopted simulation method is that it minimizes the
use of poorly known model parameters (such as source–time
functions or detailed crustal structure), by replacing them with
well-tested empirical representations. For example, the source
radiation is modeled with a general point-source spectrum
rather than through records of small earthquakes; the latter
rarely represent exact source conditions at the location of interest. Similarly, instead of relying on a crustal structure model
which is not known in much detail, path effects are modeled
through a region-specific empirical attenuation and duration
model, which takes into account the general characteristics of
wave propagation from hundreds of local earthquakes.
The adopted finite-fault simulation method has been successfully tested against observed near-field ground motions at
rock sites from the M8.0 1985 Michoacan, Mexico, the M8.0
1985 Valparaíso, Chile, and the M5.8 1988 Saguenay, Quebec, earthquakes (Beresnev and Atkinson 1997). The level of
0
5
0
-5
-10
-15
-20
-5
0
modeled low-frequency amplitudes is well constrained by the
conservation of moment of the target event. The high-frequency level is principally controlled by the corner frequency
of the subfault spectra, which is related to the subfault dimensions. Validation studies showed that the model defined in this
way successfully reproduces recorded ground motions from M
~ 8.0 subduction-zone events at periods of 0.1–4 Hz (Beresnev
and Atkinson 1997, Figs. 6 and 10), which covers most of the
frequency range of engineering interest. An accuracy of 10%
to 20% for specified ruptures is achieved, limited chiefly by
the unpredictability of the geometry and rupture parameters of
future earthquakes.
Subduction scenario
Hyndman and Wang (1995) used a compilation of geodetic,
gravity, and thermal data to place constraints on the spatial
extension of possible rupture for future Cascadia subduction
zone earthquakes. The seismogenic zone was divided into two
principal areas: (i) the fully locked zone, which is accumulating strain and will eventually rupture, due to exceedence of the
material strength; and (ii) the transition zone, which allows
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Atkinson and Beresnev
Fig. 10. The Cascadia subduction zone of western North America.
The areas of the locked and transition zones on the subduction
thrust fault are shown after Hyndman and Wang (1995). The
surface projection of the fault plane for the scenario M8.5
earthquake is indicated by a rectangle.
Table 2. Modeling parameters for hypothetical Cascadia great
earthquake.
Parameter
Fault orientation
Fault dimensions along strike and
dip (km)
Depth range (km)
Magnitude
Moment (dyne-cm)a
Stress parameter (bar)b
Subfault dimensions (km)
Subfault moment (dyne-cm)
Number of subfaults on fault plane
Number of subsources summed
Subfault rise time (s)
Subfault corner frequency (Hz)
Distance-dependent duration, Td (s)
Q(f)
Geometric spreading
Windowing function
fm (Hz)
Crustal shear-wave velocity (km/s)
Crustal density (g/cm3)
a
b
limited aseismic creep due to plasticity induced by rising temperatures. Below the transition zone, high temperatures cause
free slip that prevents strain accumulation, limiting the downward extent of the seismogenic zone. Figure 10 shows the
structure of the seismogenic zone as inferred by Hyndman and
Wang (1995). Stippled areas bounded by solid lines show the
locked and transition zones derived from geodetic data, and the
thick short lines show their limits inferred from thermal analysis, with the bands indicating estimated uncertainties. Critical
temperatures of 350°C and 450°C correspond to the onset of
plasticity and the free-slip regimes, respectively. The widths of
the locked and transition zones range from 35 + 35 km for
central Oregon to northern California, to 90 + 90 km for the
northern Washington profile. The southern Vancouver Island
margin has widths of 60 + 60 km. The authors infer the short
downdip extension of the Cascadia seismogenic zone, compared to other subduction zones, which they attribute to the
peculiarities of the regional thermal regime.
The narrow width of the seismogenic zone limits the maxi-
Value
Strike 340°, dip 10°
300 by 160
5–33
8.5
6.3 × 1028
30
25 by 20
3.4 × 1026
96
192
3.2
0.08
1.4 (R ≤ 50 km)
–2.1 + 0.07R (R > 50 km)
380f 0.39
1/R
Boxcar
15
3.7
2.8
1 dyne = 10 µN.
1 bar =100 kPa.
mum earthquake size. However, Hyndman and Wang (1995)
estimated that events of moment magnitude over 8 are possible. If the whole Cascadia seismogenic zone (including all of
the locked and transition zones) fails in a single event, empirical fault-area versus magnitude relations would suggest an
earthquake of about magnitude 9. In the simulations of this
study, we adopt the magnitude M = 8.5.
The scenario M8.5 earthquake breaks the maximum width
of the seismogenic zone, covering both the locked and the
transition zones, thus representing the maximum hazard to the
cities of western British Columbia. The fault area is 300 km
along strike and 160 km downdip (Fig. 10), with strike and dip
of 340° and 10°, respectively. The upper edge of the fault is at
a depth of 5 km. Further extension of the fault plane to the
north is not warranted by the geophysical data, while an extension to the south will not affect ground motions in the areas
of interest.
To represent uncertainty in the pattern of strain release in
future earthquakes, four possible rupture scenarios are considered. In the first model, the slip is distributed homogeneously
over the fault plane. In the second and third models, 75% of
the slip occurs in the upper and lower half of the fault, respectively. In these three cases, the rupture initiates at the centre of
the fault. To model the effects of unilateral rupture propagation
(which produces the strongest directivity effects), a fourth
model is considered, in which rupture starts at the upper southern corner of the fault and propagates towards the north, with
a slip distribution identical to that of model 3.
Ground motions for the scenario Cascadia ruptures are
simulated for Vancouver, Victoria, Tofino, and Prince George.
Their locations with respect to the fault are indicated in
Fig. 10.
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Can. J. Civ. Eng. Vol. 25, 1998
Fig. 11. Five-percent-damped pseudo-acceleration (PSA) response spectra and acceleration time histories for the M8.5 hypothesized Cascadia
subduction zone earthquake for (a) Vancouver, (b) Victoria, (c) Tofino, and (d) Prince George. Response spectra and time histories are shown
for the four rupture scenarios explained in the text. Peak ground accelerations in cm/s2 are shown above each accelerogram. All curves are
generated for the Class B “firm ground” condition. The thick solid lines on the response spectral plots show the ground motion estimates for a
M8.2 Cascadia earthquake adopted by Adams et al. (1996).
Parameters for simulations
The model parameters for the Cascadia subduction simulations
are summarized in Table 2. The fault is discretized into 96 elements, 25 by 20 km each. Summation of 192 subsources is
required to obtain the target moment; the number of triggerings
of individual subfaults is controlled by an individual slipdistribution scenario (Beresnev and Atkinson 1997, p. 71).
The stress parameter controlling the relationship between moment and slip on a subfault (static stress drop) is 30 bars (1 bar =
105 N/m2), or the average value for subduction-zone events
(Kanamori and Anderson 1975). This value agrees well with
inferred Brune stress drops for regional earthquakes (Dewberry and Crosson 1995; Atkinson 1995a). Note that the stressparameter value is not critical to the analysis; it is used only to
assign moment to subevents (Beresnev and Atkinson 1997,
pp. 71, 82). Empirical distance-dependent duration Td, path
attenuation Q, and geometric spreading models match those
used in the western point-source simulations; they are well
constrained by hundreds of earthquake recordings from the
Cascadia region (Atkinson 1995a).
The adopted high-frequency spectral cut-off parameter fm
is 15 Hz, characteristic of western North America (Boore
1983). As for the crustal earthquake simulations above, ampli-
fication for Class B ground conditions is included, using the
multiplicative factors of Fig. 1. Note that the ground response
for the Cascadia scenario (and all other simulations) is assumed linear, since the peak acceleration levels generated in
the simulations do not generally exceed the threshold for the
onset of appreciable nonlinear behavior, which is between 100
and 200 cm/s2 for soft soils and larger for firm soils (Beresnev
and Wen 1997).
Response spectra and time histories
Figures 11a–11d present 5% damped pseudo-acceleration response spectra and acceleration time histories for the M8.5
Cascadia subduction zone earthquake for Vancouver, Victoria,
Tofino, and Prince George, all for Class B sites. Response
spectra at each site are shown for the four rupture scenarios
described above, illustrating scatter of ground-motion characteristics due to uncertainty in the slip distribution and hypocentre for future events. Also given in Fig. 11 are the median (50th
percentile) response spectra estimated by Adams et al. (1996)
for a M8.2 Cascadia subduction earthquake, which were based
on the empirical ground-motion relationships of Crouse
(1991). Note that the Adams et al. spectra are not target spectra
in this case. The object of the simulations is to model the
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315
Fig. 11 (continued).
motions from a Cascadia subduction earthquake in a more
physical and region-specific manner than can be achieved by
simply applying a global attenuation relationship. The spectra
of Adams et al. are thus provided for comparison, rather than
as a target.
Figures 11a–11d suggest that the uncertainty in the response spectral values caused by a variety of possible earthquake scenarios does not exceed a factor of 2 on average. The
highest spectral amplitudes for the Cascadia earthquake are
predicted for Tofino, located just north of the projection of the
fault plane. Ground-motion durations at Vancouver and Victoria are of the order of 80–90 s, for a hypocentre located near
the centre of the fault; durations are only about 40 s at Tofino,
due to its position along the strike of the fault plane. Durations
are conspicuously shorter and spectral amplitudes generally
higher in all locations for the case of unilateral north–south
rupture; this is a pure directivity effect. Slip concentration in
the lower half of the fault also leads to generally higher amplitudes of motion, because of the proximity of the lower part
of the subduction zone to the coastal areas and its low dip
angle.
The spectra of the simulated ground motions are fairly consistent with those given by the global empirical relations used
by GSC, for Vancouver, Victoria, and Tofino. The GSC spectra are slightly lower at long periods, which may be partly
attributable to the lower moment of the target event used by
the GSC. It should be noted that the GSC spectra are not well
constrained at long periods, since reliable empirical data are
lacking at long periods in the underlying Crouse (1991) database. This study therefore suggests that the GSC spectra for
the Cascadia subduction scenario may be unconservative at
long periods. The spectra are essentially identical in the intermediate-period range. The agreement is best for Victoria and
Tofino, the locations closest to the fault. The remaining discrepancies may reflect differences in regional attenuation between Cascadia and other subduction regimes, since the
empirical relations used by GSC (Crouse 1991) are based on
ground-motion data from other subduction zones around the
world.
There is almost an order of magnitude difference between
our predictions for Prince George and those of the GSC at short
periods, whereas the curves converge at long periods. Our result is readily understood in terms of frequency-dependent
anelastic attenuation (Q-factor), which prevents high frequencies from propagating to very long distances (Prince George
is hundreds of kilometres from the fault rupture). The shape of
the response spectra necessarily changes with distance, with
the maxima shifting to longer periods as the signal propagates.
This feature can be seen from a comparison of Fig. 11d with
Figs. 11a–11c, and is noted in empirical studies throughout the
world (e.g., Boore et al. 1993; Atkinson and Boore 1995,
1997a). It is puzzling that this behavior is not seen in the GSC
spectra, where the response spectral shape remains essentially
unchanged by the effects of attenuation; this suggests that there
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Can. J. Civ. Eng. Vol. 25, 1998
Fig. 11 (continued).
may be a basic problem with applying the empirical Crouse
relations to large distances. The synthetic accelerograms for
Prince George have a distinct low-frequency content (Fig. 11d);
the duration for the first three scenarios is greater than 100 s,
due to the long crustal path. Peak ground accelerations do not
exceed 4.5 cm/s2, and the difference in response spectra for the
four scenarios is negligible.
Conclusions
Ground-motion time histories, which are compatible with the
1/500 p.a. uniform hazard spectra provided by the new national seismic hazard maps of the Geological Survey of Canada (Adams et al. 1996), have been simulated for selected
Canadian cities. The simulations provide a realistic representation of ground motion for the earthquake magnitudes and
distances that contribute most strongly to hazard at the selected
cities. Engineering analyses by time-history methods can be
performed for structures in these cities simply by using the
simulated records indicated in Table 1 (4 records are required
for each location), scaled by multiplying every point by the
“fine-tuning” factors given in Table 1. These records, based on
point-source simulations of crustal (and in some cases subcrustal) earthquake sources, have spectra that match the target
1/500 p.a. UHS of the new national seismic hazard maps, when
considered as a suite. The simulated records have amplitudes
and frequency content that are consistent with seismological
observations for earthquakes within the specific regions.
For western cities, there is an additional hazard due to the
possible occurrence of great earthquakes on the Cascadia subduction zone. Simulated time histories are provided at selected
western cities for a scenario event of M8.5 on the subduction
zone, using a finite-fault simulation methodology to consider
the variability in motions due to different possible rupture scenarios.
The ground motions simulated for the scenario M8.5 subduction event are not associated with a specific probability
level. Current information (Atwater et al. 1995) suggests that
the probability of these ground motions is comparable to that
of the 1/500 p.a. UHS generated for the new national seismic
hazard maps (the maps do not specifically include the Cascadia
subduction hazard). Thus it would be within the spirit of the
hazard maps to perform engineering analyses for buildings
in western cities for both the crustal time histories given in
Table 1 and the Cascadia scenario time histories. All time histories generated in this study are available free of charge to
interested parties, by sending an addressed, formatted 3.5” disk
to the first author, or by e-mail to gma@ccs.carleton.ca.
On a cautionary note, the time histories reflect a seismological evaluation conducted at a regional overview level, consistent with the NBCC spectra. They are not intended to replace
detailed site-specific seismological studies for important structures, for which seismic design may be a major engineering
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317
Fig. 11 (concluded).
and economic factor. In such cases, time histories can more
appropriately be developed as a component of a comprehensive site-specific seismic hazard analysis.
Acknowledgements
This research was funded by the Natural Sciences and Engineering Research Council of Canada. Two anonymous reviewers for the journal provided constructive comments.
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